Question

The value of $\underset{x\to 3}{lim}\frac{x^5-3^5}{x^8-3^8}$ is equal to

• A. $\frac{5}{8}$
• B. $\frac{5}{64}$
• C. $\frac{5}{216}$
• D. $\frac{1}{27}$
• E. $\frac{1}{63}$

Answer 1

The correct option is C $\frac{5}{216}$

$\underset{x\to 3}{lim}\frac{x^5-3^5}{x^8-3^8}$ $\left(\text{form}\frac{0}{0}\right)$
$=\underset{x\to 3}{lim}\frac{5x^4}{8x^7}$ (L Hospital's rule)
$=\underset{x\to 3}{lim}\frac{5}{8\times 3^3}=\frac{5}{8\times 27}=\frac{5}{216}$